Connecting all vertices in polygon face
If you have an n-gon face, then you can get a triangulated representation of that face using the following method (Bridge Edge Loops):


Select the object with this n-gon face.
Go into edit mode (Tab).
Go into Face Select mode.
Select the n-gon face.
X >> Only Faces.
Go into Edge Select mode.
Select the edges that make up the perimeter of the original n-gon.
Visually De-Select two opposing edges.
W >> E.






After getting more feedback from the comments, Is this more along the lines of what you are after?: